Limiting Loss Distribution of Default and Prepayment for Loan Portfolios and Its Application in RMBS

Chenxi Xia, Xin Zang (), Lan Bu, Qinhan Duan and Jingping Yang
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Chenxi Xia: School of Mathematical Sciences, Peking University, Beijing 100871, China
Xin Zang: School of Mathematics and Statistics, Beijing Jiaotong University, Beijing 100044, China
Lan Bu: Financial Technology Thrust, Hong Kong University of Science and Technology, Guangzhou 511400, China
Qinhan Duan: School of Mathematical Sciences, Peking University, Beijing 100871, China
Jingping Yang: School of Mathematical Sciences, Peking University, Beijing 100871, China

Risks, 2025, vol. 13, issue 8, 1-32

Abstract: This paper studies the joint distribution of the default and prepayment losses for a large portfolio of loans, based on a bottom-up approach. The repayment behaviors of loans in the portfolio are determined by both systematic and idiosyncratic risk factors and are conditionally independent given the systematic factors. The joint two-dimensional limit distributions of the portfolio default and prepayment losses are obtained, including the strong law of large numbers and the central limit theorem. A numerical study for the portfolio losses is performed for some simplified models. Finally, we conduct the empirical analysis on the residential mortgage-backed security (RMBS) based on Freddie Mac’s dataset. The empirical results reveal the impacts of different factors on the default and prepayment behaviors, and the distributions of the portfolio losses are simulated based on empirical estimation results to show its difference with the log-normal distributions.

Keywords: loan portfolio; default risk; prepayment risk; limiting loss distribution; RMBS (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2025
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